In recent years, a titanium oxide having a monoclinic β-type structure (represented as TiO2 (B)) has received attention as an active material for non-aqueous electrolyte batteries (see JP-A 2008-34368 (KOKAI), JP-A 2008-117625 (KOKAI) and WO2009/028553A1). In a spinel-type lithium titanate (Li4Ti5O12) that has been actually used since before, the number of lithium ions that can be inserted and desorbed per a unit chemical formula is three. Therefore, the number of lithium ions that can be inserted and desorbed per one titanium ion was ⅗, and 0.6 was the theoretical maximum. In this regard, the number of lithium ions in TiO2 (B), which can be inserted and released per a titanium ion is 1.0 at the maximum. Therefore, TiO2 (B) has a property that the theoretical capacity is as high as about 335 mAh/g.